Prime Minister Theresa May had sent Gavin Williamson, her chief whip, to Belfast to lead talks with the party's officials. Later, Downing Street confirmed that the DUP agreed to the principles of an outline agreement to support the Conservatives on a confidence and supply basis.
The DUP said talks would continue next week to "work on the details" and "reach agreement".
Earlier, May had expressed her regret at the huge losses the Conservative party suffered? winning just 318 seats, well short of the 326 overall majority.
The DUP won 10 seats in the election which pushes Mrs.
And those bigoted views run through the party to this day - Paisley's son and North Antrim MP, Ian Paisley Jr, said in 2007 that he's "pretty repulsed" by gay people, and claimed that they "harm society".
Scottish Conservative leader Ruth Davidson has since sought assurances from May that any deal with the DUP would not affect LGBTI (Lesbian, Gay, Bisexual, Transgender, and/or Intersex) rights across the UK.
In London, hundreds gathered at Parliament Square Saturday to protest the Tory-DUP alliance, with many calling for May's resignation.
Alastair Ross, a former DUP member of the legislative assembly in Northern Ireland, told BBC Radio Ulster's Inside Politics he would not expect a deal to last more than 12 or 18 months.
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A small political party entirely based in Northern Ireland that has been out of the spotlight for years could emerge as a decisive force in allowing the Conservative Party to form a majority in the House of Commons after Theresa May's disastrous campaign result in the 2017 general election.
The party's founder Ian Paisley spearheaded the Save Ulster from Sodomy in the 1970s, which was opposed to the decriminalisation of homosexuality in Northern Ireland, in fact, Northern Ireland was the last country within the United Kingdom to decriminalise homosexuality, which it did so in 1982.
Commitments made in the Democratic Unionist Party (DUP) manifesto are likely to put the party at odds with the Conservatives when it comes to pension policies.
She came to prominence after resigning over the "cash for ash" scandal, having overseen a government programme that misused public funds.
The nursery worker said he was "angry" that Mrs May had done a deal with the DUP, although he admitted he did not initially know who they were.
These deals tend to be loose and a long way short of a formal coalition.
While Mrs May has already told the Queen she has a workable Commons majority, there have been suggestions that the Queen may not deliver a speech if a question mark remains over whether it will get voted through.
There is also anger among the party membership over the huge election losses and May's gamble to call a snap general election a full three years ahead of when it would have been officially due in 2020.
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